Kontsevich invariant

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In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral[1] of an oriented framed link, is a universal Vassiliev invariant[2] in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients. It was defined by Maxim Kontsevich.

The Kontsevich invariant is a universal quantum invariant in the sense that any quantum invariant may be recovered by substituting the appropriate weight system into any Jacobi diagram.

Definition[edit]

The Kontsevich invariant is defined by monodromy along solutions of the Knizhnik–Zamolodchikov equations.

References[edit]

  1. ^ Chmutov, Sergei; Duzhi, Sergei (2012). Weisstein, Eric W, ed. "Kontsevich Integral". Mathworld (Wolfram Web Resource). Retrieved 4 December 2012. 
  2. ^ Kontsevich, Maxim (1993). "Vassiliev's knot invariants". Adv. Soviet Math 16 (2): 137. 

Bibliography[edit]